Parametrische Auswertung unvollst�ndiger chromatographischer Trennungen mit dem FORTRAN-Programm CHROMA nach einer Bi-Gauss-Approximation

1972 ◽  
Vol 261 (4-5) ◽  
pp. 369-376
Author(s):  
H. Pratzel
Keyword(s):  
Gauss Approximation

scholarly journals GAUSS APPROXIMATION FOR NUMBER DISTRIBUTION IN OF A PASCAL’S TRIANGLE

2021 ◽  
pp. 10-19
Author(s):  
I. M. Abramov ◽  
G. S. Abramov
Keyword(s):  
Normal Distribution ◽  
Chemical Processes ◽  
Experimental Methodology ◽  
Pascal’S Triangle ◽  
Number Distribution ◽  
Central Elements ◽  
Distribution Parameters ◽  
Pascal's Triangle ◽  
Multinomial Coefficients ◽  
Gauss Approximation

We received normal distribution parameters that approximates the distribution of numbers in the n-th row of Pascal's triangle. We calculated the values for normalized moments of even orders and shown their asymptotic tendency towards values corresponding to a normal distribution. We have received highly accurate approximations for central elements of even rows of Pascal's triangle, which allows for calculation of binomial, as well as trinomial (or, in general cases, multinomial) coefficients. A hypothesis is proposed, according to which it is possible that physical and physics-chemical processes function according to Pascal's distribution, but due to how slight its deviation is from a normal distribution, it is difficult to notice. It is also possible that as technology and experimental methodology improves, this difference will become noticeable where it is traditionally considered that a normal distribution is taking place.

scholarly journals Necessary conditions for the propagation of two modes, LP01 and LP11, in a step-index optical fiber with a Kerr nonlinearity

2020 ◽  
Vol 44 (4) ◽  
pp. 533-539
Author(s):  
V.A. Burdin ◽  
A.V. Bourdine ◽  
O.Yu. Gubareva
Keyword(s):  
Finite Elements ◽  
Optical Fiber ◽  
Approximate Formula ◽  
Necessary Conditions ◽  
Mixed Finite Elements ◽  
Kerr Nonlinearity ◽  
Optical Pulses ◽  
Step Index ◽  
Upper Limit ◽  
Gauss Approximation

This paper presents the results of an analysis of the necessary propagation conditions in a step-index optical fiber with a Kerr nonlinearity of two modes, LP01 and LP11, during the transmission of high-power optical pulses. All results were obtained by solving a system of two nonlinear equations for these modes, obtained by the Gauss approximation method, and the subsequent use of a procedure for refining estimates using the mixed finite elements method. The necessary conditions are determined, estimates of the boundaries for the range of normalised frequencies for which they are fulfilled are obtained, and an approximate formula is proposed for estimating the upper limit of this range.

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